Two-dimensional invariant manifolds and global bifurcations: Some approximation and visualization studies

Mark E. Johnson, Michael S. Jolly, Ioannis G. Kevrekidis

Research output: Contribution to journalArticle

46 Scopus citations

Abstract

We illustrate and discuss the computer-assisted study (approximation and visualization) of two-dimensional (un)stable manifolds of steady states and saddle-type limit cycles for flows in Rn. Our investigation highlights a number of computational issues arising in this task, along with our solutions and "quick-fixes" for some of these problems. Two examples illustrative of both successes and shortcomings of our current approach are presented. Representative "snapshots" demonstrate the dependence of two-dimensional invariant manifolds on a bifurcation parameter as well as their interactions. Such approximation and visualization studies are a necessary component of the computer-assisted study and understanding of global bifurcations.

Original languageEnglish (US)
Pages (from-to)125-140
Number of pages16
JournalNumerical Algorithms
Volume14
Issue number1-3
DOIs
StatePublished - Jan 1 1997

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • Computational dynamics
  • Global bifurcations
  • Invariant manifolds

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